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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Figure P5.31 shows a two-reservoir water supply system. The water level in reservoir 1 drops at the rate of \(0.01 \mathrm{~m} / \mathrm{min}\), and the water level in reservoir 2 drops at the rate
The Hoover Dam backs up the Colorado River and creates Lake Mead, which is approximately 115 miles long and has a surface area of approximately 225 square miles. If during flood conditions the
Storm sewer backup causes your basement to flood at the steady rate of 1 in. of depth per hour. The basement floor area is \(1500 \mathrm{ft}^{2}\). What capacity (gal/min) pump would you rent to (a)
The Wide World of Fluids article "Green" 1.6-gpf standards,". When a toilet is flushed, the water depth, \(h\), in the tank as a function of time, \(t\), is as given in the table. The size of the
Find the force components \(F_{x}\) and \(F_{y}\) required to hold the box shown in Fig. P5.35 stationary. The fluid is oil and has specific gravity of 0.85. Neglect gravity effects. Atmospheric
When a baseball player catches a ball, the force of the ball on her glove is as shown as a function of time in Fig. P5.36. Describe how this situation is similar to the force generated by the
Find the horizontal and vertical forces to hold stationary the nozzle shown in Fig. P5.37. The fluid flowing through it is \(10{ }^{\circ} \mathrm{C}\) liquid water; \(A_{1}=1.0 \mathrm{~m}^{2},
Water flows through a horizontal bend and discharges into the atmosphere as shown in Fig. P5.38. When the pressure gage reads 10 psi, the resultant \(x\)-direction anchoring force, \(F_{A x}\), in
Find the magnitude of the force \(F\) required to hold the plate in Fig. P5.39 stationary.Figure P5.39 V = 30 m/s m = 5 kg/s Water 45 F
Water enters the horizontal, circular cross-sectional, sudden contraction nozzle sketched in Fig. P5.40 at section (1) with a uniformly distributed velocity of \(25 \mathrm{ft} / \mathrm{s}\) and a
A truck carrying chickens is too heavy for a bridge that it needs to cross. The empty truck is within the weight limits; with the chickens it is overweight. It is suggested that if one could get the
Exhaust (assumed to have the properties of standard air) leaves the 4-ft-diameter chimney shown in Video V5.4 and Fig. P5.42 with a speed of \(6 \mathrm{ft} / \mathrm{s}\). Because of the wind, after
Air at \(T_{1}=300 \mathrm{~K}, p_{1}=303 \mathrm{kPa}\), and \(V_{1}=0.5 \mathrm{~m} / \mathrm{s}\) enters the Venturi shown in Fig. P5.43. The air leaves at \(T_{2}=220 \mathrm{~K}\) and \(p_{2}=\)
Water flows steadily from a tank mounted on a cart as shown in Fig. P5.44. After the water jet leaves the nozzle of the tank, it falls and strikes a vane attached to another cart. The cart's wheels
Determine the magnitude and direction of the anchoring force needed to hold the horizontal elbow and nozzle combination shown in Fig. P5.45 in place. Atmospheric pressure is \(100
Figure P5.46 shows a lateral pipe fitting. This particular fitting has a mainline diameter of \(4.0 \mathrm{in}\). The diameter of the lateral is \(3.0 \mathrm{in}\)., and the lateral angle is
Water flows steadily between fixed vanes, as shown in Fig. P5.47. Find the \(x\) and \(y\) components of the water's force on the vanes. The total volume flow rate is \(100 \mathrm{~m}^{3} /
The hydraulic dredge shown in Fig. P5.48 is used to dredge sand from a river bottom. Estimate the thrust needed from the propeller to hold the boat stationary. Assume the specific gravity of the
A static thrust stand is to be designed for testing a specific jet engine, knowing the following conditions for a typical test.\[ \begin{aligned} \text { intake air velocity } & =700 \mathrm{ft} /
A vertical jet of water leaves a nozzle at a speed of \(10 \mathrm{~m} / \mathrm{s}\) and a diameter of \(20 \mathrm{~mm}\). It suspends a plate having a mass of \(1.5 \mathrm{~kg}\) as indicated in
A horizontal, circular cross-sectional jet of air having a diameter of 6 in. strikes a conical deflector as shown in Fig. P5.51. A horizontal anchoring force of \(5 \mathrm{lb}\) is required to hold
Calculate the pressure change \(\left(p_{2}-p_{1}\right)\) for the jet pump shown in Fig. P5.52. The fluid is \(20{ }^{\circ} \mathrm{C}\) water. Assume negligible friction at the walls and uniform
Air flows into the atmosphere from a nozzle and strikes a vertical plate as shown in Fig. P5.53. A horizontal force of \(12 \mathrm{~N}\) is required to hold the plate in place. Determine the reading
Water flows from a large tank into a dish as shown in Fig. P5.54. (a) If at the instant shown the tank and the water in it weigh \(W_{1} \mathrm{lb}\), what is the tension, \(T_{1}\), in the cable
Figure P5.55 shows the configuration of the center (tailmounted) jet engine on an airliner. The airliner is cruising at altitude, and the velocities shown are relative to an observer on board.
The plate shown in Fig. P5.56 is \(0.5 \mathrm{~m}\) wide perpendicular to the paper. Calculate the velocity of the water jet required to hold the plate upright.Figure P5.56 d = 10.0 cm 20C water jet
Two water jets of equal size and speed strike each other as shown in Fig. P5.57. Determine the speed, \(V\), and direction, \(\theta\), of the resulting combined jet. Gravity is negligible.Figure
Figure P5.58 shows coal being dropped from a hopper onto a conveyor belt at a constant rate of \(25 \mathrm{ft}^{3} / \mathrm{s}\). The coal has a specific gravity ranging from 1.12 to 1.50. The belt
Determine the magnitude of the horizontal component of the anchoring force required to hold in place the sluice gate shown in Fig. 5.59. Compare this result with the size of the horizontal component
Water flows steadily into and out of a tank that sits on frictionless wheels as shown in Fig. P5.60. Determine the diameter \(D\) so that the tank remains motionless if \(F=0\).Figure P5.60 TD
The rocket shown in Fig. P5.61 is held stationary by the horizontal force, \(F_{x}\), and the vertical force, \(F_{z}\). The velocity and pressure of the exhaust gas are \(5000 \mathrm{ft} /
Air discharges from a 2-in.-diameter nozzle and strikes a curved vane, which is in a vertical plane as shown in Fig. P5.62. A stagnation tube connected to a water U-tube manometer is located in the
Water is sprayed radially outward over \(180^{\circ}\) as indicated in Fig. P5.63. The jet sheet is in the horizontal plane. If the jet velocity at the nozzle exit is \(20 \mathrm{ft} / \mathrm{s}\),
A sheet of water of uniform thickness \((h=0.01 \mathrm{~m})\) flows from the device shown in Fig. P5.64. The water enters vertically through the inlet pipe and exits horizontally with a speed that
The results of a wind tunnel test to determine the drag on a body (see Fig. P5.65) are summarized below. The upstream [section (1)] velocity is uniform at \(100 \mathrm{ft} / \mathrm{s}\). The static
A variable mesh screen produces a linear and axisymmetric velocity profile as indicated in Fig. P5.66 in the airflow through a 2 -ft-diameter circular cross-sectional duct. The static pressures
Consider unsteady flow in the constant diameter, horizontal pipe shown in Fig. P5.67. The velocity is uniform throughout the entire pipe, but it is a function of time: \(\mathbf{V}=u(t)
In a turbulent pipe flow that is fully developed, the axial velocity profile is,\[ u=u_{c}\left[1-\left(\frac{r}{R}\right)\right]^{1 / 7} \]as is illustrated in Fig. P5.68. Compare the axial
Water from a garden hose is sprayed against your car to rinse dirt from it. Estimate the force that the water exerts on the car. List all assumptions and show calculations.
A Pelton wheel vane directs a horizontal, circular crosssectional jet of water symmetrically as indicated in Fig. P5.70 and Video V5.6. The jet leaves the nozzle with a velocity of \(100 \mathrm{ft}
The thrust developed to propel the jet ski shown in Video V9.18 and Fig. P5.71 is a result of water pumped through the vehicle and exiting as a high-speed water jet. For the conditions shown in the
Thrust vector control is a technique that can be used to greatly improve the maneuverability of military fighter aircraft. It consists of using a set of vanes in the exit of a jet engine to deflect
The exhaust gas from the rocket shown in Fig. P5.73a leaves the nozzle with a uniform velocity parallel to the \(x\) axis. The gas is assumed to be discharged from the nozzle as a free jet. (a) Show
The Wide World of Fluids article titled "Where the Plume goes,". Air flows into the jet engine shown in Fig. P5.74 at a rate of 9 slugs/s and a speed of \(300 \mathrm{ft} / \mathrm{s}\). Upon
Figure P5.75 shows a sharp-edged splitter plate used to control the flow of a liquid jet \(W\) units wide by \(H_{1}\) units high. Write expressions for the deflection angle \(\theta\) and the force
The Wide World of Fluids article titled "Motorized Surfboard,". The thrust to propel the powered surfboard shown in Fig. P5.76 is a result of water pumped through the board that exits as a high-speed
The Wide World of Fluids article titled "Bow Thrusters,".The bow thruster on the boat shown in Fig. P5.77 is used to turn the boat. The thruster produces a \(1-\mathrm{m}\)-diameter jet of water with
Water flows from a two-dimensional open channel and is diverted by an inclined plate as illustrated in Fig. P5.78. When the velocity at section (1) is \(10 \mathrm{ft} / \mathrm{s}\), what horizontal
If a valve in a pipe is suddenly closed, a large pressure surge may develop. For example, when the electrically operated shutoff valve in a dishwasher closes quickly, the pipes supplying the
A snowplow mounted on a truck clears a path \(12 \mathrm{ft}\) through heavy wet snow, as shown in Figure P5.80. The snow is 8 in. deep and its density is \(10 \mathrm{lbm} / \mathrm{ft}^{3}\). The
An incompressible fluid flows outward through a blower as indicated in Fig. P5.81. The shaft torque involved, \(T_{\text {shaft }}\), is estimated with the following relationship:\[ T_{\text {shaft
Water at \(60^{\circ} \mathrm{F}\) is flowing through the 2 -in. steel pipe shown in Fig. P5.82 at the rate of \(90 \mathrm{gal} / \mathrm{min}\). Determine the torque developed at the base where the
Five liters/s of water enter the rotor shown in Video V5.10 and Fig. P5.83 along the axis of rotation. The crosssectional area of each of the three nozzle exits normal to the relative velocity is
Figure P5.84 shows a simplified sketch of a dish-washer water supply manifold. Find the resisting torque for a water temperature of \(140^{\circ} \mathrm{F}\). \(Q=0.25 \mathrm{gal} / \mathrm{min}\)
The hydraulic turbine shown in Fig. P5.85 has a \(10{ }^{\circ} \mathrm{C}\) water flow rate of \(36.4 \mathrm{~m}^{3} / \mathrm{s}\), an inlet radius \(R_{1}=1.0 \mathrm{~m}\), an outlet radius
A fan (see Fig. P5.86) has a bladed rotor of 12 -in. outside diameter and 5-in. inside diameter and runs at \(1725 \mathrm{rpm}\). The width of each rotor blade is \(1 \mathrm{in}\). from blade inlet
Calculate the torque required to drive the pump shown in Fig. P5.87 at \(30 \mathrm{~Hz}\) and to deliver \(20{ }^{\circ} \mathrm{C}\) water at \(3.0 \mathrm{~m}^{3} / \mathrm{min}\).Figure P5.87
An axial flow turbomachine rotor involves the upstream (1) and downstream (2) velocity triangles shown in Fig. P5.88. Is this turbomachine a turbine or a fan? Sketch an appropriate blade section and
An inward flow radial turbine (see Fig. P5.89) involves a nozzle angle, \(\alpha_{1}\), of \(60^{\circ}\) and an inlet rotor tip speed, \(U_{1}\), of \(6 \mathrm{~m} / \mathrm{s}\). The ratio of
A sketch of the arithmetic mean radius blade sections of an axial-flow water turbine stage is shown in Fig. P5.90. The rotor speed is \(1000 \mathrm{rpm}\). (a) Sketch and label velocity triangles
Distinguish between shaft work and other kinds of work associated with a flowing fluid.
An incompressible fluid flows along a \(0.20-\mathrm{m}\)-diameter pipe with a uniform velocity of \(3 \mathrm{~m} / \mathrm{s}\). If the pressure drop between the upstream and downstream sections of
A horizontal Venturi flow meter consists of a convergingdiverging conduit as indicated in Fig. P5.93. The diameters of cross sections (1) and (2) are 6 and \(4 \mathrm{in}\). The velocity and static
Figure P5.94 shows the mixing of two streams. The shear stress between each fluid and its adjacent walls is negligible. Why can't Bernoulli's equation be applied between points in stream 1 and the
Liquid water at \(40^{\circ} \mathrm{F}\) flows down a vertical, thermally insulated, 2 -in. steel pipe. The temperature change of the water is related to its internal energy change by\[
A simplified schematic drawing of the carburetor of a gasoline \((S=0.75)\) engine is shown in Fig. P5.96. The throat area is \(0.5 \mathrm{in.}^{2}\). The running engine draws air downward through
Oil \((S G=0.9)\) flows downward through a vertical pipe contraction as shown in Fig. P5.97. If the mercury manometer reading, \(h\), is \(100 \mathrm{~mm}\), determine the volume flowrate for
An incompressible liquid flows steadily along the pipe shown in Fig. P5.98. Determine the direction of flow and the head loss over the 6-m length of pipe.Figure P5.98 0.75 m 1.0 m 6 m 1.5 m 3 m
A siphon is used to draw water at \(70^{\circ} \mathrm{F}\) from a large container as indicated in Fig. P5.99. The inside diameter of the siphon line is \(1 \mathrm{in}\). and the pipe centerline
A water siphon having a constant inside diameter of 3 in. is arranged as shown in Fig. P5.100. If the friction loss between \(A\) and \(B\) is \(0.8 V^{2} / 2\), where \(V\) is the velocity of flow
Figure P5.101 shows a test rig for evaluating the loss coefficient, \(\mathrm{K}\), for a valve. Mechanical energy losses in valves are modeled by the equation:\[ g
For the \(180^{\circ}\) elbow and nozzle flow shown in Fig. P5.102, determine the loss in available energy from section (1) to section (2). How much additional available energy is lost from section
An automobile engine will work best when the back pressure at the interface of the exhaust manifold and the engine block is minimized. Show how reduction of losses in the exhaust manifold, piping,
(See The Wide World of Fluids article titled "Smart Shocks," Section 5.3.3.) A 200-lb force applied to the end of the piston of the shock absorber shown in Fig. P5.104 causes the two ends of the
Based on flowrate and pressure rise information, estimate the power output of a human heart.
Oil \((S G=0.88)\) flows in an inclined pipe at a rate of \(5 \mathrm{ft}^{3} / \mathrm{s}\) as shown in Fig. P5.106. If the differential reading in the mercury manometer is \(3 \mathrm{ft}\),
The pumper truck shown in Fig. P5.107 is to deliver \(1.5 \mathrm{ft}^{3} / \mathrm{s}\) to a maximum elevation of \(60 \mathrm{ft}\) above the hydrant. The pressure at the 4-in.-diameter outlet of
The hydroelectric turbine shown in Fig. P5.108 passesFigure P5.108 600 ft Turbine
A pump is to move water from a lake into a large, pressurized tank as shown in Fig. P5.109 at a rate of \(1000 \mathrm{gal}\) in \(10 \mathrm{~min}\) or less. Will a pump that adds \(3 \mathrm{hp}\)
Water is pumped from the tank shown in Fig. P5.110a. The head loss is known to be \(1.2 V^{2} / 2 g\), where \(V\) is the average velocity in the pipe. According to the pump manufacturer, the
Water is pumped steadily through the apparatus shown in Fig. P5.111. The pipe area and gage pressure are shown for both outlet sections 1 and 2. Assume that the \(40^{\circ} \mathrm{F}\) water is
Water is pumped from the large tank shown in Fig. P5.112. The head loss is known to be equal to \(4 V^{2} / 2 g\) and the pump head is \(h_{p}=20-4 Q^{2}\), where \(h_{p}\) is in \(\mathrm{ft}\) when
Water flows by gravity from one lake to another as sketched in Fig. P5.113 at the steady rate of \(80 \mathrm{gpm}\). What is the loss in available energy associated with this flow? If this same
The turbine shown in Fig. P5.114 develops \(100 \mathrm{hp}\) when the flowrate of water is \(20 \mathrm{ft}^{3} / \mathrm{s}\). If all losses are negligible, determine(a) the elevation \(h\),(b) the
Figure P5.115 shows a pump testing setup. Water is drawn from a sump and pumped through a pipe containing a valve. The water is discharged into a catch tank sitting on a scale. During a test run,
Water is to be moved from one large reservoir to another at a higher elevation as indicated in Fig. P5.116. The loss of available energy associated with \(2.5 \mathrm{ft}^{3} / \mathrm{s}\) being
Determine the volume flow rate and minimum power input to the water pump in Fig. P5.117. Determine the actual power if the hydraulic efficiency is \(75 \%\) and losses in the motor and bearings are
A pump moves water horizontally at a rate of \(0.02 \mathrm{~m}^{3} / \mathrm{s}\). Upstream of the pump where the pipe diameter is \(90 \mathrm{~mm}\), the pressure is \(120 \mathrm{kPa}\).
Water is to be pumped from the large tank shown in Fig. P5.119 with an exit velocity of \(6 \mathrm{~m} / \mathrm{s}\). It was determined that the original pump (pump 1) that supplies \(1
The Wide World of Fluids article titled "Curtain of Air,". The fan shown in Fig. P5.120 produces an air curtain to separate a loading dock from a cold storage room. The air curtain is a jet of air
When the pump shown in Fig. P5.121 is stopped, there is no flow through the system and the spring force is zero. With the pump running, a 6 -in.-diameter jet leaves the pipe, and the spring force is
Air flows past an object in a pipe of 2-m diameter and exits as a free jet as shown in Fig. P5.122. The velocity and pressure upstream are uniform at \(10 \mathrm{~m} / \mathrm{s}\) and \(50
Near the downstream end of a river spillway, a hydraulic jump often forms, as illustrated in Fig. P5.123 and Video V10.11. The velocity of the channel flow is reduced abruptly across the jump. Using
Water flows steadily down the inclined pipe as indicated in Fig P5.124. Determine the following: (a) the difference in pressure \(p_{1}-p_{2}\), (b) the loss between sections (1) and (2), (c) the net
When fluid flows through an abrupt expansion as indicated in Fig. P5.125, the loss in available energy across the expansion, \(\operatorname{loss}_{\mathrm{ex}}\), is often expressed as\[
Water \(\left(60{ }^{\circ} \mathrm{F}\right)\) flows through an annular space formed by inserting a 1 -in.-radius solid cylinder into a 1.5-in.-radius tube. The following axial velocities were
Find the acceleration of the cart shown in Fig. P5.127 as a function of the water height in the cart, which varies with time. The initial total mass is \(m_{0}\), and the fluid density is \(ho_{0}\).
Two water jets collide and form one homogeneous jet as shown in Fig. P5.128. (a) Determine the speed, \(V\), and direction, \(\theta\), of the combined jet. (b) Determine the loss for a fluid
Water flows vertically upward in a circular cross-sectional pipe. At section (1), the velocity profile over the cross-sectional area is uniform. At section (2), the velocity profile is\[
Calculate the kinetic energy correction factor for each of the following velocity profiles for a circular pipe:(a) \(u=u_{\max }\left(1-\frac{r}{R}\right)\)(b) \(u=u_{\max

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